@Article{CiCP-18-1313,
author = {},
title = {An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {5},
pages = {1313--1335},
abstract = {<p style="text-align: justify;">The paper aims to develop an effective preconditioner and conduct the convergence
analysis of the corresponding preconditioned GMRES for the solution of discrete
problems originating from multi-group radiation diffusion equations. We firstly
investigate the performances of the most widely used preconditioners (ILU(k) and
AMG) and their combinations ($B_{co}$ and&nbsp;$\widetilde{B}_{co}$), and provide drawbacks on their feasibilities.
Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing
the features suitable for AMG using more detailed measurements on multiscale
nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present
an adaptive combined preconditioner $B^α_{co}$ involving an improved ILU(0) along with
its convergence constraints. Numerical results demonstrate that <span style="text-align: justify;">$B^α_{co}$</span>-GMRES holds the
best robustness and efficiency. At last, we analyze the convergence of GMRES with
combined preconditioning which not only provides a persuasive support for our proposed
algorithms, but also updates the existing estimation theory on condition numbers
of combined preconditioned systems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.091014.060315a},
url = {http://global-sci.org/intro/article_detail/cicp/11070.html}
}